The accurate control and specification of color in color display devices (for example, color CRT monitors, printers, copiers and the like) is important to those who utilize color displays. Part of the effort to meet these control and specification needs has been the development of color spaces that describe, in some useful way, the gamut of colors that can be produced by the particular display device. The coordinates of the color space are made available to the user for selection of the coordinates that correspond to a particular color.
One widely used color space, known as the video RGB color system, is employed with a cathode-ray tube (CRT) color display. The video RGB color system is directly related to the hardware of the CRT display, namely, the three electron guns that are used to address the three primary color phosphors ("primaries") carried on the CRT screen. The three primary phosphors emit red, green and blue light, respectively. A CRT display is an additive color system and a gamut of colors can be created by controlling the various intensities of the red, green and blue light emitted by the phosphors. The intensities of the phosphors are controlled by altering the beam current of the corresponding electron gun.
The video RGB color system is represented as a cube-shaped color space having a black point at one corner and a white point at the diagonally opposing corner. The black point corresponds to the absence of emissions from all three phosphors; the white point being the combined full intensity of all three phosphors as excited by the three electron guns. Emanating from the black point in a mutually orthogonal relationship (i.e., in a cartesian coordinate system) are three axes respectively corresponding to the red, green and blue phosphor intensities. Each axis terminates at the full intensity of the associated phosphor. Each axis carries coordinates commonly referred to as "DAC values", which are numerical values corresponding to the electron gun control level required to drive the associated phosphor at a particular intensity. DAC values can be specified to generate any color within the space.
The video RGB system is widely used because it is based upon the hardware (electron guns and associated drive circuitry) employed for creating the color display. However, it is important to note that the video RGB system does not provide perceptually uniform color space. That is, at various locations within the space, a selected change in the DAC values will not necessarily result in a commensurate perceived change in the displayed color. For example, changing the DAC values to move n units in one region of the space may result in no perceived color change, while a move of n units in another region of the space may yield a substantial perceived change. The perceptual nonuniformity of the video RGB system is a result of the nonlinearity of human vision in perceiving the color spectrum. The effect of the perceptual nonuniformity of the video RGB system is that it is difficult for the user to predict what color will appear for any given change in DAC values.
In the past, numerous efforts have been made to develop useful perceptually uniform color spaces for facilitating color specification tasks. Many efforts to develop perceptually uniform color spaces have also been directed to correlating the color spaces to internationally accepted standards for color measurement so that the color can be accurately communicated and consistently reproduced. The most prominent international standards for color measurement are collectively termed the CIE system (Commission International de l'Eclairage or International Commission on Illumination).
The CIE system is based on the premise that specific perceived colors result from the proper combination of an illuminant or reference light source, an object, and an observer. A useful explanation of the CIE system is provided in "Principles of Color Technology", 2nd ed. 1981, by Billmeyer & Saltzman. Generally, the CIE system defines standard light sources having a characteristic spectral power distribution curve. That curve is a depiction of the relative luminous power of the source, i.e., the amount of light associated with each wavelength of the visible spectrum. The CIE system also defines a "standard observer" in terms of three color matching functions. In graphical form, the color matching functions are the relative magnitudes of three standard stimuli necessary to produce any color. Any object, the color of which is to be specified, has a characteristic spectral reflectance curve. The reflectance curve is a representation of the fraction of the light reflected from the object at each wavelength. As is known, the product of the spectral power distribution curve for a standard source and the reflectance curve of the object under study, when separately multiplied by each color matching function will, after suitable normalization, yield three curves, the area under each curve corresponding respectively to the CIE tristimulus values XYZ. The values of the standard stimuli that define the color matching functions are such that the color matching function corresponding to the Y tristimulus value represents the human eye response to the total power of the light (i.e., luminance) reaching the eye. Accordingly, the tristimulus value Y provides an indication of the luminance of the color.
The CIE tristimulus values have been converted to a two-dimensional map of colors known as the 1931 CIE chromaticity diagram. The 1931 diagram is shown in FIG. 1 and includes a horseshoe-shaped spectrum locus with the spectral colors identified on the locus by their wavelengths. The coordinates of the chromaticity diagram are known as chromaticity coordinates x and y, and are derived by taking the ratios of the respective X and Y tristimulus values to the sum of all three tristimulus values X, Y and Z. The x and y chromaticity coordinates for any real color are located within the bounds of the spectrum locus and the line that joins the ends of the spectrum locus.
The x and y coordinates do not completely describe a color because they contain no information on the inherent luminance of a color. As noted, the Y component of the tristimulus values is a measure of the luminance of the color. Accordingly a three-dimensional color specification system is created by adding a third axis to the 1931 diagram which extends upwardly from the xy plane at the x and y coordinates of the source light. The third axis is the Y axis and is scaled in units of luminance. For scaling purposes, it is conventional to normalize the Y values from 0 to 1, representing the full range from black to white, respectively. At each level of luminance the area of the 1931 diagram, which represents the range of colors that can occur, becomes smaller for increasing values of Y and terminates at a single "white point" at the maximum Y value.
The three-dimensional color specification system just described is known as the CIExyY system. In view of the above, it can be appreciated that any real color can be specified in terms of the CIExyY color specification system and directly related to the particular CIE tristimulus values XYZ. The CIExyY system, which is based upon the 1931 CIE chromaticity diagram (and related tristimulus values XYZ), is a widely accepted method for specifying color. Further, the 1931 diagram or, more typically, data derived therefrom, is valuable because it can be used to predict the additive mixture of two or more colors. That is, tristimulus values of component colors mathematically add to yield the tristimulus values of the resulting mixed color.
Efforts have been made to transform the CIE color specification system into perceptually uniform color spaces, while preserving the additive mixing feature of the 1931 CIE chromaticity diagram.
One such transformation of the 1931 diagram includes a two dimensional uniform chromaticity diagram (known as the CIE 1976 UCS diagram) having u' and v' coordinates that approximate a perceptually uniform color plane. The coordinates are known as the uniform chromaticity coordinates and are directly related to the x and y chromaticity coordinates (hence, to the XYZ tristimulus values) as follows: EQU u'=4x/(-2x+12y+3)=4X/(X+15Y+3Z) (1) EQU v'=9y/(-2x+12y+3)=9Y/(X+15Y+3Z) (2)
As described, in the referenced text by Billmeyer & Saltzman, the 1976 UCS diagram defined by the u' and v' coordinates has been mathematically converted into a color space that closely approaches perceptual uniformity. That color space is known as the CIELUV color space.
The CIELUV space is characterized by u*, v* coordinate axes. These axes were defined with the achromatic colors at the origin (u*=0, v*=0) by subtracting the uniform chromaticity values u'.sub.n and v'.sub.n for the source light from those of the selected color.
The third coordinate of the CIELUV space, L*, known as the metric lightness function, lies perpendicular to the u*v* plane and intersects that plane at the origin. The L* axis is the axis of the achromatic colors (black, grey and white) and denotes variations in the lightness from L*=0 (black) to L*=100 (white).
As noted, all of the coordinates of the CIELUV space are directly related, via the CIExyY system to the CIE tristimulus values. These relationships are defined below: ##EQU1## where
Y=tristimulus value (luminance) of a color, and
Y.sub.n =luminance of the reference light source EQU u*=13 L* (u'-u'.sub.n) (5) EQU v*=13 L* (v'-v'.sub.n) (6)
where
u'.sub.n and v'.sub.n are the uniform chromaticity coordinates for the reference light source.
The modified cube-root function for L* as shown above, yields a perceptually uniform scaling of lightness. It is common to refer to the visual sensation of lightness as value.
Hue is defined in the CIELUV color space as the angle made relative to the positive u* axis. The hue angle, h*, is defined as follows: EQU h*=arctan (v*/u*) (7)
A third notation, known as the psychometric chroma C*.sub.uv, is adopted in conjunction with the CIELUV color space as a numerical representation of the chroma of a color. Chroma describes the saturation or vibrancy of a color, which is its distance from the L* axis at a particular level of lightness or value. Accordingly, the notation C*.sub.uv, relates to the u*, v* coordinates, as follows: EQU C*.sub.uv =(u*.sup.2 +v*.sup.2).sup.1/2 ( 8)
The CIELUV space is the most nearly perceptually uniform space developed thus far. Particularly, away from the boundaries of the space, equal physical distances along any given dimension of hue, lightness, or chroma are representative of substantially uniform perceived color differences. As an example, it is convenient to examine a circle of hues taken at a constant level of lightness and chroma. Color pairs sampled from this hue circle, that are 5.degree. apart from one another will be perceived as having the same magnitude of color difference, regardless of the hue family or overall position in the color space. The color difference, .DELTA.E.sub.uv, can be quantified in terms of the CIELUV coordinates as follows: EQU .DELTA.E.sub.uv =[(.DELTA.L*).sup.2 +(.DELTA.v*).sup.2 +(.DELTA.u*).sup.2 ].sup.1/2 ( 9)
wherein the values .DELTA.L*, .DELTA.u* and .DELTA.v* represent the magnitude of the differences between those coordinates for the color pair.
It can be appreciated that the theoretical advantages of the CIELUV system can be effectively exploited by one interested in specifying a color from it if there is provided a useful method for reversibly transforming conventional color space coordinates, such as the video RGB system coordinates, into the CIELUV coordinates. Further, it has been found that for colors displayed by a CRT or other display device, modification of the CIELUV color space is desirable to produce a new color space with enhanced perceptual uniformity, and which is defined by the actual gamut of colors that can be produced by the CRT display device.